Modeling Compositions of Impedance-based Primitives via Dynamical Systems

In this work, we introduce a novel Dynamical System (DS)-based approach for modeling complex and compliant manipulation tasks, that are composed of a sequence of action phases with different compliance requirements; i.e. impedance primitives. We adopt a closed-loop (DS)-based control architecture and present the Locally Active Globally Stable (LAGS)-DS formulation. In LAGS-DS we seek to model the whole task as a globally asymptotically stable DS that has locally task-varying dynamics and smoothly transit between them. These locally task-varying dynamics represent the set of impedance primitives, hence, rather than modeling the task as a discretization of impedance primitives, we model it as a composition of impedance primitives in a single DS-based controller. In this paper, we present the theoretical background for this novel DS, briefly describe the learning approach and provide 2D simulations of LAGS-DS learned from toy data.